Multilevel Inverse-Based Factorization Preconditioner for Solving Sparse Linear Systems in Electromagnetics

Authors

  • Yiming Bu 1 Institute of Mathematics and Computer Science, University of Groningen, Groningen, 9712 CP, The Netherlands , 2 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731
  • Bruno Carpentieri School of Science and Technology, Nottingham Trent University, Burton Street, Nottingham NG1 4BU, UK
  • Zhaoli Shen 1 Institute of Mathematics and Computer Science, University of Groningen, Groningen, 9712 CP, The Netherlands , 2 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731
  • Tingzhu Huang School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731 China

Keywords:

Approximate inverse preconditioners, computational electromagnetics, Krylov subspace methods, sparse matrices

Abstract

We introduce an algebraic recursive multilevel approximate inverse-based preconditioner, based on a distributed Schur complement formulation. The proposed preconditioner combines recursive combinatorial algorithms and multilevel mechanisms to maximize sparsity during the factorization.

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References

Y. Bu, B. Carpentieri, Z. Shen, and T.-Z. Huang, “A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems,” Applied Numerical Mathematics, vol. 104, pp. 141-157, 2016.

G. Karypis and V. Kumar, “A fast and high quality multilevel scheme for partitioning irregular graphs,” SIAM J. Sci. Comput., vol. 20, pp. 359-392, 1999.

T. Davis, Sparse Matrix Collection, (1994). Available at the URL: http: //www.cise.ufl.edu/ research/sparse/matrices

Y. Saad, Iterative Methods for Sparse Linear Systems. SIAM Publications, 2nd edition, 2003.

Y. Saad and B. Suchomel, “ARMS: An algebraic recursive multilevel solver for general sparse linear systems,” Numer. Linear Algebra Appl., vol. 9, no. 5, pp. 359-378, 2002.

M. Grote and T. Huckle, “Parallel preconditionings with sparse approximate inverses,” SIAM J. Sci. Comput., vol. 18, pp. 838-853, 1997.

M. Bollhoefer, Y. Saad, and O. Schenk, ILUPACK - Preconditioning Software Package, 2010. Available online at the URL: http://ilupack.tu-bs.de.

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Published

2021-07-25

How to Cite

[1]
Yiming Bu, Bruno Carpentieri, Zhaoli Shen, and Tingzhu Huang, “Multilevel Inverse-Based Factorization Preconditioner for Solving Sparse Linear Systems in Electromagnetics”, ACES Journal, vol. 33, no. 02, pp. 160–163, Jul. 2021.

Issue

2018: Vol 33 Iss 2

Section

Articles